oazeta | R Documentation |

Fits a one-altered zeta distribution based on a conditional model involving a Bernoulli distribution and a 1-truncated zeta distribution.

```
oazeta(lpobs1 = "logitlink", lshape = "loglink",
type.fitted = c("mean", "shape", "pobs1", "onempobs1"),
gshape = exp((-4:3)/4), ishape = NULL, ipobs1 = NULL, zero = NULL)
```

`lpobs1` |
Link function for the parameter |

`lshape` |
See |

`type.fitted` |
See |

`gshape, ishape, ipobs1, zero` |
See |

The response `Y`

is one with probability `p_1`

,
or `Y`

has a 1-truncated zeta distribution with
probability `1-p_1`

. Thus `0 < p_1 < 1`

,
which is modelled as a function of the covariates. The one-altered
zeta distribution differs from the one-inflated
zeta distribution in that the former has ones coming from one
source, whereas the latter has ones coming from the zeta
distribution too. The one-inflated zeta distribution
is implemented in the VGAM package. Some people
call the one-altered zeta a *hurdle* model.

The input can be a matrix (multiple responses).
By default, the two linear/additive predictors
of `oazeta`

are `(logit(\phi), log(shape))^T`

.

An object of class `"vglmff"`

(see `vglmff-class`

).
The object is used by modelling functions such as `vglm`

,
and `vgam`

.

The `fitted.values`

slot of the fitted object,
which should be extracted by the generic function `fitted`

, returns
the mean `\mu`

(default) which is given by

`\mu = \phi + (1-\phi) A`

where `A`

is the mean of the one-truncated
zeta distribution.
If `type.fitted = "pobs1"`

then `p_1`

is returned.

This family function effectively combines
`binomialff`

and
`otzeta`

into
one family function.

T. W. Yee

`Oazeta`

,
`zetaff`

,
`oizeta`

,
`otzeta`

,
`CommonVGAMffArguments`

,
`simulate.vlm`

.

```
## Not run: odata <- data.frame(x2 = runif(nn <- 1000))
odata <- transform(odata, pobs1 = logitlink(-1 + 2*x2, inverse = TRUE),
shape = loglink( 1 + 1*x2, inverse = TRUE))
odata <- transform(odata, y1 = roazeta(nn, shape = shape, pobs1 = pobs1),
y2 = roazeta(nn, shape = shape, pobs1 = pobs1))
with(odata, table(y1))
ofit <- vglm(cbind(y1, y2) ~ x2, oazeta, data = odata, trace = TRUE)
coef(ofit, matrix = TRUE)
head(fitted(ofit))
head(predict(ofit))
summary(ofit)
## End(Not run)
```

VGAMdata documentation built on Sept. 18, 2023, 9:08 a.m.

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